Correct.
Driver always opens.
To close, Guard beeps 2-1. Driver Closes. Guard shuts local door, then either gives two or platform staff activate RA.
The (alleged) train in question did use platform 5.
That's the procedure for Voyagers (the correct bell-buzzer code being 1-2 rather than 2-1). Pendolino doors are closed by the Train Manager using a close doors button provided in each door panel.
Wrong side door releases aren't common but not unheard of. Typically more common where the driver opens the doors but does happen from time to time on conductor-operated services too.
It's important to of course remember that such an incident isn't necessarily a mistake by the staff involved - although in this case if the train was permitted to continue the likelihood is it probably was, as if a fault was suspected then the train would be taken out of service for inspection.
In terms of answering the question asked by the OP, what procedure would be applied, generally (procedures will slightly differ between TOCs) along the lines of:
Close the erroneously opened doors
Report the incident to the signaller and control
If it's not confirmed as human error then arrangements would be made to take the unit out of traffic to check for safety-related faults
If it is confirmed as human error then a check would be made as to whether the driver is able to continue (look at incident history etc)
If the driver can continue then check their welfare and make sure they think they're fit to do so. If the driver can't continue then control to arrange relief.
Company procedures might require drug and alcohol screening for the Driver, if thats the case then control make arrangements for this to take place.
Driver and Train Manager provide reports into the incident.
Incident will be recorded on the Driver's safety of the line file and in industry systems.
Someone somewhere will decide whether it just needs a basic review of the incident or whether it needs a full investigation.
Investigation will consider evidence such as the crew's reports, CCTV, on-train data recorder downloads etc to identify causes and whether any lessons can be learnt or changes made.
Someone will be allocated to sort out those changes.
Hopefully there'll be less chance of the incident happening again.